CN107480352A - A kind of reliability optimization method of Milling Process technological parameter - Google Patents

A kind of reliability optimization method of Milling Process technological parameter Download PDF

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CN107480352A
CN107480352A CN201710631126.2A CN201710631126A CN107480352A CN 107480352 A CN107480352 A CN 107480352A CN 201710631126 A CN201710631126 A CN 201710631126A CN 107480352 A CN107480352 A CN 107480352A
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黄贤振
李庆伟
张义民
李常有
朱丽莎
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Northeastern University China
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Abstract

The present invention provides a kind of reliability optimization method of Milling Process technological parameter, including：Step S1, the optimized variable and optimization aim of Milling Process technological parameter are determined；Step S2, according to predetermined constraints and optimized variable, optimization aim, multi objective function optimization model is established；The constraints includes：Milling system reliability constraint；Step S3, processing is optimized to the multi objective function optimization model using the method that genetic algorithm and Non-Linear Programming are combined, the Milling Process technological parameter after being optimized.The above method can preferably reduce manufacture and processing cost requirement.

Description

A kind of reliability optimization method of Milling Process technological parameter
Technical field
The present invention relates to Machine Manufacturing Technology, and in particular to a kind of reliability optimization method of Milling Process technological parameter.
Background technology
High-rate wireless LAN technology already turns into the important component of advanced manufacturing technology, while is also advanced manufacture skill Most important basic technology in art.High-rate wireless LAN has the advantages that high accuracy, great surface quality and high material removing rate, Thus it is widely used in the fields such as space flight and aviation, automobile, ship, the energy, track traffic.But in recent years, along with modern work The rapid development of industry and the pressure of market competition gradually increase, and engineering goods are intended to become privileged, complex-shaped, thin-wall construction, The problems such as difficult-to-machine material is more cause crudy and precision to be difficult to control.Grasp high accuracy, the high efficiency of complicated vital part Manufacturing technology turns into the important topic that China's manufacturing industry faces.
High-rate wireless LAN is premised on stablizing milling, and the research to stability of high-speed milling is to promote high-speed milling Process technology is using an important topic with development.Occur in Milling Processes, between lathe, cutter and workpiece violent Vibration, the lighter can influence crudy, reduce production efficiency, and severe one causes the generation of production accident, jeopardizes the person and enterprise Industry safety.Milling vibration can be divided into forced vibration and the major class of self-excited vibration two, and wherein most important vibration mode, and be most difficult to The vibration mode of control is exactly flutter, and the forced vibration as caused by the amount of feeding is to produce the principal element of Surface Location Error. Therefore, milling stability analysis and the theoretical research of Optimization of Milling Parameters are carried out, the high property of Digit Control Machine Tool can be better achieved Can be with high-precision Milling Process.
At present, the stability that the research of milling stability is concentrated mainly under different processing methods and processing conditions is ground Study carefully, mainly using the recommendation without flutter Limit cutting depth as Optimization of Milling Parameters, lack and stability and Optimized model depth are melted The analysis of conjunction.Furthermore the Milling Parameters after optimization do not account for the reliability of milling system, it is likely that obtained parameter can make whole Individual milling system is in the edge of failure, no matter have greatly to system life-span itself, the even personal safety of converted products quality Influence.Traditional optimization method does not take many actual conditions in Milling Processes into account, it is difficult to ensures high milling Cut parameter optimization precision.
The content of the invention
To solve the problems of the prior art, the present invention provides a kind of reliability optimization side of Milling Process technological parameter Method, it can preferably reduce manufacture and processing cost requirement.
In a first aspect, the present invention provides a kind of reliability optimization method of Milling Process technological parameter, including：
Step S1, the optimized variable and optimization aim of Milling Process technological parameter are determined；
Step S2, according to predetermined constraints and optimized variable, optimization aim, multi objective function optimization model is established； The constraints includes：Milling system reliability constraint；
Step S3, the multi objective function optimization model is entered using the method that genetic algorithm and Non-Linear Programming are combined Row optimization processing, the Milling Process technological parameter after being optimized.
Alternatively, in step sl,
Optimized variable includes：X=(vc,ft,ap,ae)；
Wherein, vcRepresent cutting speed m/min, apRepresent axial cutting-in mm, ftRepresent feed engagement mm/z and aeRepresent Radial direction cutting-in mm；
Optimization aim is：The maximum production efficiency that minimal surface site error SLE and material removing rate MRR is represented；
MRR=Ω Napaeft；
N represents cutter tooth number.
Alternatively, in step s 2,
Multi objective function optimization model is：
Constraints is：
p5(x)=apmin-x3≤0
p6(x)=x3-apmax≤0
p7(x)=aemin-x4≤0
p8(x)=x4-aemax≤0
R≥Rmin
Ω represents machine spindle speed, vfRepresent the feed speed of lathe, TmaxThe maximum cutting that representing lathe allows is turned round Square, PmaxThe maximum admissible power of lathe is represented, R represents the reliability of milling system, RminFor the reliability of minimum allowable, FtTable Show cutting force, D represents milling cutter diameter, x1,2,3,4The 1st, 2,3,4 parameter of X variables is represented,
Wherein, X=(vc,ft,ap,ae)；Initial value according to the stable region of predetermined the stability lobes diagram choose accord with Close the numerical value of stability.
Alternatively, the step S2 includes：
The constraints of multi objective function optimization model is handled using Means of Penalty Function Methods, by the multiple objective function Constraint Anchored Optimization corresponding to Optimized model is converted to a unconfinement Optimized model；
Correspondingly, in step s3, initial Milling Parameters are chosen by default the stability lobes diagram, judges initial milling Whether the stability reliability of parameter meets milling system reliability constraint, if so, then using genetic algorithm and non-linear Plan that the method being combined optimizes processing to the object function in the unconfinement Optimized model, the milling after being optimized Working process parameter.
Alternatively, step S2 includes：
Punished according to the relation construction between milling stability, milling Surface Location Error reliability and default optimized variable Penalty function：
P(vc,ft,ap,ae)=Mk·(max(0,R1min-R1(vc,ft,ap,ae))
+max(0,R2min-R2(vc,ft,ap,ae)))
Wherein, R1For stability reliability, R2For Surface Location Error reliability, MkFor penalty factor, vcCutting speed (m/min)、apAxial cutting-in (mm), feed engagement ftAnd radial direction cutting-in a (mm/z)e(mm)；
Use penalty handle after final optimization pass object function for：
Fun=-MRR+SLE+Mk·(max(0,R1min-R1(vc,ft,ap,ae))
+max(0,R2min-R2(vc,ft,ap,ae)))
Constraints is：
Alternatively, the step S2 includes：
The minimal surface site error model established using approximate shceme Forecasting Methodology in the multi objective function optimization model.
Alternatively, miss the minimal surface position established using approximate shceme Forecasting Methodology in the multi objective function optimization model Differential mode type, including：
Obtained using approximate shceme Forecasting Methodology and establish transfer matrix corresponding to the stability of milling parameter Stability Model；
Judge the characteristic value of transfer matrix；
If the characteristic value of transfer matrix, in Milling Process system stable region, milling parameter stability mould is established in acquisition Stable state coefficient during type；
Minimal surface site error model is obtained according to the stable state coefficient.
Alternatively, the minimal surface site error model is handled using Kriging model optimizations, obtains reliability, sentence Whether disconnected reliability meets Reliability Constraint condition, if satisfied, then
Parameter corresponding to final result will be tried to achieve, as the Milling Process technological parameter after optimization.
Alternatively, it is described before the step of handling the minimal surface site error model using Kriging model optimizations Method also includes：
Predetermined number sample point is obtained using mixed sampling method, using genetic algorithm to the θ in initial Kriging models Optimize, Kriging models are built using the θ after the predetermined number sample point and optimization.
Alternatively, Kriging models are built, including：
Judge whether the sampling dimension of minimal surface site error model is more than 1；
If so, predetermined number sample point is then obtained using the Latin Hypercube Sampling method of amendment；
Otherwise, predetermined number sample point is obtained using Han Mosili sequential samplings method；
The maximum value position of the M-EI in minimal surface site error model is determined using improved global optimization method；
Judge whether to meet stopping criterion, if so, then utilizing the θ structures after the predetermined number sample point and optimization Kriging models；
Otherwise, by it is determined that maximum value position at obtain sample point add sample set, rebuild Kriging moulds Type.
It is the device have the advantages that as follows：
Using material removing rate and Surface Location Error as the object function of optimization in the method for the present invention, propose that one kind exists Ensure that milling system reliability is not less than under conditions of a certain setting, the Optimization of Milling Parameters mould under the conditions of stable constraint Type；Also, in the calculating of reliability, using high-precision Kriging agent models, not only increase computational accuracy, efficiency Also greatly improve.Using the inventive method compared with existing conventional method, it can preferably reduce manufacture and processing cost will Ask, there is highly important construction value.
Brief description of the drawings
Figure 1A and Figure 1B is respectively the method implementation process figure of the present invention；
Fig. 2 is the Dynamic Model of Milling Process figure of the present invention；
Fig. 3 is the implementation process figure of the mixed sampling of the present invention；
Fig. 4 is the M-EI algorithm flow charts of the Kriging models of the present invention.
Embodiment
In order to preferably explain the present invention, in order to understand, below in conjunction with the accompanying drawings, by embodiment, to this hair It is bright to be described in detail.
All of technologies and scientific terms used here by the article and the those skilled in the art for belonging to the present invention are usual The implication of understanding is identical.Term used in the description of the invention herein is intended merely to describe specific embodiment Purpose, it is not intended that in the limitation present invention.Term as used herein " and/or " include one or more related Listed Items Arbitrary and all combination.
As shown in Figure 1A, the embodiment of the present invention provides a kind of reliability optimization method of Milling Process technological parameter, the party Method comprises the steps：
Step S1, the optimized variable and optimization aim of Milling Process technological parameter are determined.
For example, optimized variable includes：X=(vc,ft,ap,ae)；
Wherein, vcRepresent cutting speed m/min, apRepresent axial cutting-in mm, ftRepresent feed engagement mm/z and aeRepresent Radial direction cutting-in mm；
Optimization aim can be：The maximum production efficiency that minimal surface site error SLE and material removing rate MRR is represented；
MRR=Ω Napaeft；N represents cutter tooth number.
Step S2, according to predetermined constraints and optimized variable, optimization aim, multi objective function optimization model is established； The constraints includes：Milling system reliability constraint
It will be appreciated that in the present embodiment, the multi objective function optimization model can be established using approximate shceme Forecasting Methodology In minimal surface site error model.
In the present embodiment, multi objective function optimization model is：
Constraints can be：
R≥Rmin
Ω represents machine spindle speed, vfThe feed speed of lathe is represented, the maximum cutting that Tmax represents lathe and allowed is turned round Square, Pmax* represent the maximum admissible power of lathe, and R represents the reliability of milling system, RminFor the reliability of minimum allowable, Ft Cutting force is represented, D represents milling cutter diameter, x1,2,3,4The 1st, 2,3,4 parameter of X variables is represented,
Wherein, X=(vc,ft,ap,ae)；Initial value according to the stable region of predetermined the stability lobes diagram choose accord with Close the numerical value of stability.
Step S3, the multi objective function optimization model is entered using the method that genetic algorithm and Non-Linear Programming are combined Row optimization processing, the Milling Process technological parameter after being optimized.
For example, above-mentioned steps S2 may include：
S21, according to the relation structure between milling stability, milling Surface Location Error reliability and default optimized variable Make penalty：
P(vc,ft,ap,ae)=Mk·(max(0,R1min-R1(vc,ft,ap,ae))
+max(0,R2min-R2(vc,ft,ap,ae)))
Wherein, R1For stability reliability, R2For Surface Location Error reliability, MkFor penalty factor, vcCutting speed (m/min)、apAxial cutting-in (mm), feed engagement ftAnd radial direction cutting-in a (mm/z)e(mm)。
S22, using Means of Penalty Function Methods the constraints of multi objective function optimization model is handled, by the multiple target Constraint Anchored Optimization corresponding to function optimization model is converted to a unconfinement Optimized model；
Use penalty handle after final optimization pass object function for：
Fun=-MRR+SLE+Mk·(max(0,R1min-R1(vc,ft,ap,ae))
+max(0,R2min-R2(vc,ft,ap,ae)))
Constraints is：
Correspondingly, in step s3, it is excellent to the unconfinement using the method that genetic algorithm and Non-Linear Programming are combined Change model and optimize processing, the Milling Process technological parameter after being optimized.
The method of the present embodiment, is set out according to actual conditions, and stability is combined with Optimized model depth, and by reliability Reliability when making the milling system complete predetermined function to ensure the technological parameter after optimization as constraints is not less than a certain Value.Approximate shceme method is used when establishing in Data Model, and in the calculating of reliability, first by improved Kriging models It is introduced into Optimization of Milling Parameters, the target using material removing rate and Surface Location Error as optimization, with genetic algorithm and non-thread Property the algorithm that is combined of planning optimize, the parameter finally obtained has great practical value for Practical Project.
For a better understanding of the present invention, below in conjunction with Figure 1B to Fig. 4 to being described in detail.
In the present embodiment, by taking carbide helical end mill processing aluminium alloy 7075-T6 as an example, Cutting Force Coefficient is：Kt =6 × 108N/m2, Kn=2 × 108N/m2, Kte=Kne=0；Modal stiffness kx=ky=1.34 × 106N/m, modal damping cx =cy=5.089Ns/m, modal mass mx=my=0.03993kg；It is specific as shown in table 1：
The probability density characteristicses of the stochastic variable of table 1
In the present embodiment, the flow chart of method comprises the following steps as shown in Figure 1B：
Step 01, primary work are exactly the variable that selection needs to optimize, using basic cutting data parameter as design Variable, i.e. cutting speed vc(m/min), axial cutting-in ap(mm), feed engagement ftAnd radial direction cutting-in a (mm/z)e(mm), i.e., Design variable is X=(vc,ft,ap,ae)；
Step 02, optimization aim elect the production efficiency of minimal surface site error (SLE) and maximum as, wherein, production effect Rate is represented with material removing rate (Material Removal Rate, MRR)；
MRR can be expressed from the next：
MRR=Ω Napaeft (5)
Step 03, due to by the speed of mainshaft of selected lathe, the amount of feeding, centripetal force, cutting power, workpiece quality etc. limit System, it is specific as follows in order to more conform to actual requirement, it is necessary to which many constraints and influence are taken into account；
Sub-step 3-1, cutting speed vcIt must is fulfilled for machine spindle speed Ω constraint；
Sub-step 3-2, feed engagement ftIt must is fulfilled for the feed speed v of lathefConstraint；
Sub-step 3-3, the high rotating speed of high-speed milling, small cutting-in, roughing feed are obvious features, so will axially cut It is limited in certain section deeply；
Sub-step 3-4, it is same as above, radial direction cutting-in is also required to be limited in certain section；
Sub-step 3-5, the cutting moment of torque are necessarily less than the maximum cutting moment of torque of lathe permission；
Sub-step 3-6, cutting power are necessarily less than the maximum nominal power of lathe；
Sub-step 3-7, high-speed milling process in, flutter will occur when the setting of parameter is unreasonable, so Related parameter is chosen according to the stability lobes diagram.
The stability lobes diagram of the present embodiment can be the flap figure for the process generation for having been carried out milling process, be existing Flap figure.Described stable constraint is established with Surface Location Error model and can be predicted using approximate shceme method, final To the stability lobes diagram, and Milling Process parameter can only be under the curve being made up of axial cutting-in, radial direction cutting-in and the speed of mainshaft Side's selection.
Each cutting parameter and stability reliability and Surface Location Error reliability is calculated in sub-step 3-8, analysis Between relation, and ensure that reliability is more than a certain value in process；
R≥Rmin (12)
In formula, RminFor the reliability of minimum allowable.
Step 04, according to selected optimization aim, establish multi objective function optimization model；
Multi objective function optimization model is shown below：
Step 05, the Optimized model established based on step 04, the present embodiment are mutually tied using genetic algorithm with Non-Linear Programming The method of conjunction carries out reliability optimization to multi objective function optimization model；
That is, the method being combined using genetic algorithm and Non-Linear Programming carries out reliability Optimum Design.It is classical Non-Linear Programming local search ability is stronger, but ability of searching optimum is weaker.Genetic algorithm is calculated using selection, intersection and variation Son scans for, and ability of searching optimum is stronger, but local search ability is weaker.So with reference to the advantages of two kinds of algorithms, use Genetic algorithm carries out global search, while carries out Local Search using Nonlinear Programming Algorithm, to obtain the global optimum of problem Solution.
Step 06, the constraints to foundation are handled, and the present embodiment is used in indirect method than more typical punishment letter Number method carries out the processing of constraints, and existing optimization problem is converted into a unconfinement optimization problem.
In the present embodiment, will be existing using the processing for carrying out constraints in indirect method than more typical Means of Penalty Function Methods Some optimization problems are converted into a unconfinement optimization problem.Now by milling stability, milling Surface Location Error reliability with And complicated relation construction penalty is shown below between each optimized variable：
In formula, R1For stability reliability, R2For Surface Location Error reliability, MkFor penalty factor.
Correspondingly, the object function of the final optimization pass after being handled using penalty is shown below：
The present embodiment is carried out using the method that genetic algorithm and Non-Linear Programming are combined to multi objective function optimization model Reliability optimization.
It is described as follows for establishing minimal surface site error model in above-mentioned steps 02：
Minimal surface site error model is established using approximate shceme method in the present embodiment, for building for milling parameter stability It is vertical also to be realized using approximate shceme method.
It is prediction/foundation of milling parameter stability first：
Cycle T is divided into r period, i.e. T=m Δs t, m ∈ Z by sub-step 2-a, the prediction of approximate shceme method first.Cycle can It is interpreted as milling cutter to cut one week, that is, turns around.
Milling Process kinetic model is as shown in figure 1, its governing equation can be expressed as：
Wherein, m is equivalent mass；C is equivalent damping；K is equivalent stiffness；
Q (t)=[x (t) y (t)]TFor cutting tool mode coordinate, F (t)=[Fx(t) Fy(t)]TFor cutting force matrix, M is The modal mass matrix of cutter, K are modal stiffness matrix, and C is modal damping matrix.
IfAnd x (t)=[q (t) p (t)]T, now, formula (13) can change into state The form of equation
In formula (14),
At any time on section, formula (14) can be expressed as again
In formula (16) formula, tj=j Δs t, j ∈ Z.
Wherein, periodic system is severalStatus itemsAnd time lag itemIt can be tried to achieve by linear approximation, be respectively
Wherein, Bj=B (tj), yj=y (tj)。
The ODE that sub-step 2-b, solution kinetics equation are formed；
(16) are solved equation, are obtained
yj+1=(Φ0+Fj)yj+Fj+1yj+1-Fj+1yj-m+1-Fjyj-m (20)
In formula,
Φ0=eAΔt, Φ1=A-1(Φ0- I), Φ2=A-1(ΔtΦ0-Φ1), Φ3=A-1(Δt2Φ0-2Φ2) (23)
Sub-step 2-c, according to above-mentioned steps obtain discrete matrix；
zj+1=Djzj (24)
In formula (24),
zj=col (yj,yj-1,...,yj+1-m,yj-m) (25)
Sub-step 2-d, the final state-transition matrix that obtains are it is determined that milling parameter stability.
Transfer matrix is expressed as
Φ=Dm-1Dm-2...D1D0 (27)
Theoretical according to Floquet, the stability of Milling Process system can be judged by transfer matrix Φ characteristic value, if transfer The mould of matrix Φ all characteristic values is respectively less than 1, then Milling Process system is stable, i.e.,
Next to that establish minimal surface site error model：
Cycle T is divided into r period by sub-step 2-1, the prediction of approximate shceme method first；
When calculating milling Surface Location Error, it is necessary to consider the static force item in kinetics equation, now, above-mentioned formula (14) it is changed into
In formula (29), f (t)=[0 f0(t)]T。
At any time on section, formula (29) can be
Static force item in formula (30)It can equally be tried to achieve by linear approximation：
Wherein, fj=f (tj)。
The ODE that sub-step 2-2, solution kinetics equation are formed；
That is the ODE of solution formula (30) obtains
yj+1=(Φ0+Fj)yj+Fj+1yj+1-Fj+1yj-r+1-Fjyj-r+Gj (32)
In formula (32),
The rapid 2-3 of step, the calculating process in above-mentioned sub-step 2-2, obtain discrete matrix；
Following Discrete Mapping can be obtained by formula (32)
zj+1=Djzj+EjGj (34)
In formula (34),
Ej=col ([I-Fj+1]-1,0,...,0) (35)
State transfer relationship of the system on the single time cycle can be by matrix sequence Dj, Ej, Gj(j=0 ..., r-1) table Go out, i.e.,
yr=Φ y0+H (36)
In formula,
The stable state coefficient vector in l cycles can be calculated according to fixed-point principle by formula (26)：
Sub-step 2-4, finally give stable state coefficient can and obtain Surface Location Error model.
In addition, during for Reliability Constraint described in sub-step 3-8, the meter of the reliability of minimal surface site error model Calculation method is using Kriging models.And the optimization of the model of correlation has been carried out when using Kriging models, specific stream Journey figure is as shown in Figure 4：
Sub-step 3-a, with mixed sampling method initial samples particular flow sheet is carried out to minimal surface site error model As shown in figure 3, obtain certain amount sample point.
In addition, being optimized according to Kriging models to Stability Model, then mixed sampling method can be used to stable Property model carry out initial samples, to obtain certain amount sample point.
Sub-step 3-b, with genetic algorithm the θ in initial Kriging models is optimized, then utilize the sample obtained θ after point and optimization builds initial kriging models；
Sub-step 3-c, the maximum value position of M-EI (improved improve it is expected) is obtained with improved global optimization method, and And sample in this place；By the new sample point of acquisition and Kriging models are updated when being unsatisfactory for stopping criterion；
Ask concretely comprising the following steps for M-EI：
Assuming that by either objective function minxY=F (x) is modified to minxY+ks, (k >=0), because Kriging methods are one Individual universal method, so representing arbitrary power function F (x) herein, then current function minimum value is changed into,
(y+ks)min=min (yi+ksi),(si=0,1,2 ..., n) (39)
If
Then have,
Wherein,
Sub-step 3-d, with improved global optimization approach the optimal solution of current Kriging models is obtained, and in this place Valuation is sampled, final result (the higher Kriging of the final ratio of precision that is established is obtained if stop condition is met Model), Kriging models are updated if being unsatisfactory for, then go to sub-step 3-c.
The stopping criterion of this method is：
Wherein ΔsIt is off precision；And in practice, the stopping criterion generally use relative accuracy Δ of optimized algorithmr：
Embodiment
Simulation parameter number of teeth N=2, diameter D=12.7mm, milling mode are climb cutting, the kinetic parameter such as institute of table 5.1 Show.According to genetic algorithm and Nonlinear Programming Theory, programming realization is based on genetic algorithm and non-linear rule in MATLAB softwares The function optimizing algorithm drawn solves the problem.Genetic algorithm parameter is arranged to：Population scale 100, evolutionary generation 100, individual are handed over Pitch probability 0.6, individual variation probability 0.01.The front and rear Comparative result of optimization is as shown in table 2.
Finally the constraints of embodiment determination is：
The optimum results of table 2 contrast
Optimize front and rear parameter from table 2 it can be found that stability and the reliability of Surface Location Error are obtained for and carried Height, bring up to 1 by 0.998 and 0.509 respectively；And MRR has then brought up to 5682mm3/min by 3414mm3/min；Equally SLE has reduced to 0.0106mm by -0.0413mm, meets engineering actual demand.
Finally it should be noted that：Above-described embodiments are merely to illustrate the technical scheme, rather than to it Limitation；Although the present invention is described in detail with reference to the foregoing embodiments, it will be understood by those within the art that： It can still modify to the technical scheme described in previous embodiment, or which part or all technical characteristic are entered Row equivalent substitution；And these modifications or substitutions, the essence of appropriate technical solution is departed from various embodiments of the present invention technical side The scope of case.

Claims (10)

  1. A kind of 1. reliability optimization method of Milling Process technological parameter, it is characterised in that including：
    Step S1, the optimized variable and optimization aim of Milling Process technological parameter are determined；
    Step S2, according to predetermined constraints and optimized variable, optimization aim, multi objective function optimization model is established；It is described Constraints includes：Milling system reliability constraint；
    Step S3, the multi objective function optimization model is carried out using the method that genetic algorithm and Non-Linear Programming are combined excellent Change is handled, the Milling Process technological parameter after being optimized.
  2. 2. according to the method for claim 1, it is characterised in that in step sl,
    Optimized variable includes：X=(vc,ft,ap,ae)；
    Wherein, vcRepresent cutting speed m/min, apRepresent axial cutting-in mm, ftRepresent feed engagement mm/z and aeRepresent radially Cutting-in mm；
    Optimization aim is：The maximum production efficiency that minimal surface site error SLE and material removing rate MRR is represented；
    MRR=Ω Napaeft；
    N represents cutter tooth number.
  3. 3. according to the method for claim 2, it is characterised in that in step s 2,
    Multi objective function optimization model is：
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mi>min</mi> </mtd> <mtd> <mrow> <mo>&amp;lsqb;</mo> <mrow> <mo>|</mo> <mi>S</mi> <mi>L</mi> <mi>E</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mi>e</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>|</mo> <mo>,</mo> <mo>-</mo> <mi>M</mi> <mi>R</mi> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mi>e</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>v</mi> <mi>c</mi> </msub> <mo>,</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mi>p</mi> </msub> <mo>,</mo> <msub> <mi>a</mi> <mi>e</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <mn>0</mn> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mn>10</mn> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
    Constraints is：
    <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;pi;D&amp;Omega;</mi> <mi>min</mi> </msub> </mrow> <mn>1000</mn> </mfrac> <mo>-</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>&amp;le;</mo> <mn>0</mn> </mrow>
    <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>-</mo> <mfrac> <mrow> <msub> <mi>&amp;pi;D&amp;Omega;</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow> <mn>1000</mn> </mfrac> <mo>&amp;le;</mo> <mn>0</mn> </mrow>
    <mrow> <msub> <mi>p</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>f</mi> <mi>min</mi> </mrow> </msub> <mrow> <msub> <mi>N&amp;Omega;</mi> <mi>max</mi> </msub> </mrow> </mfrac> <mo>-</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>&amp;le;</mo> <mn>0</mn> </mrow>
    <mrow> <msub> <mi>p</mi> <mn>4</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>-</mo> <mfrac> <msub> <mi>v</mi> <mrow> <mi>f</mi> <mi>max</mi> </mrow> </msub> <mrow> <msub> <mi>N&amp;Omega;</mi> <mi>min</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <mn>0</mn> </mrow>
    p5(x)=apmin-x3≤0
    p6(x)=x3-apmax≤0
    p7(x)=aemin-x4≤0
    p8(x)=x4-aemax≤0
    <mrow> <msub> <mi>p</mi> <mn>9</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>F</mi> <mi>t</mi> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <mi>D</mi> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mn>1000</mn> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>T</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> </mrow>
    <mrow> <msub> <mi>p</mi> <mn>10</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>P</mi> <mo>=</mo> <msub> <mi>F</mi> <mi>t</mi> </msub> <mo>&amp;CenterDot;</mo> <mfrac> <msub> <mi>v</mi> <mi>c</mi> </msub> <mrow> <mn>60</mn> <mo>&amp;times;</mo> <mn>1000</mn> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>P</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>&amp;CenterDot;</mo> <mi>&amp;eta;</mi> </mrow>
    R≥Rmin
    Wherein, Ω represents machine spindle speed, vfRepresent the feed speed of lathe, TmaxThe maximum cutting that representing lathe allows is turned round Square, PmaxThe maximum admissible power of lathe is represented, R represents the reliability of milling system, RminFor the reliability of minimum allowable, FtTable Show cutting force, D represents milling cutter diameter, x1,2,3,4The 1st, 2,3,4 parameter of X variables is represented,
    Wherein, X=(vc,ft,ap,ae)；Initial value chosen according to the stable region of predetermined the stability lobes diagram meet it is steady Qualitatively numerical value.
  4. 4. according to the method for claim 3, it is characterised in that the step S2 includes：
    The constraints of multi objective function optimization model is handled using Means of Penalty Function Methods, by the multi objective function optimization Constraint Anchored Optimization corresponding to model is converted to a unconfinement Optimized model；
    Correspondingly, in step s3, initial Milling Parameters are chosen by default the stability lobes diagram, judges initial Milling Parameters Stability reliability whether meet milling system reliability constraint, if so, then using genetic algorithm and Non-Linear Programming The method being combined optimizes processing to the object function in the unconfinement Optimized model, the Milling Process after being optimized Technological parameter.
  5. 5. according to the method for claim 4, it is characterised in that step S2 includes：
    According to the relation construction punishment letter between milling stability, milling Surface Location Error reliability and default optimized variable Number：
    P(vc,ft,ap,ae)=Mk·(max(0,R1min-R1(vc,ft,ap,ae))
    +max(0,R2min-R2(vc,ft,ap,ae)))
    Wherein, R1For stability reliability, R2For Surface Location Error reliability, MkFor penalty factor, vcCutting speed (m/ min)、apAxial cutting-in (mm), feed engagement ftAnd radial direction cutting-in a (mm/z)e(mm)；
    Use penalty handle after final optimization pass object function for：
    Fun=-MRR+SLE+Mk·(max(0,R1min-R1(vc,ft,ap,ae))
    +max(0,R2min-R2(vc,ft,ap,ae)))
    Constraints is：
    <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mn>420</mn> <mo>&amp;le;</mo> <msub> <mi>v</mi> <mi>c</mi> </msub> <mo>&amp;le;</mo> <mn>600</mn> <mi>m</mi> <mi>m</mi> <mo>/</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0.02</mn> <mo>&amp;le;</mo> <msub> <mi>f</mi> <mi>t</mi> </msub> <mo>&amp;le;</mo> <mn>0.08</mn> <mi>m</mi> <mi>m</mi> <mo>/</mo> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>0.2</mn> <mo>&amp;le;</mo> <msub> <mi>a</mi> <mi>p</mi> </msub> <mo>&amp;le;</mo> <mn>0.8</mn> <mi>m</mi> <mi>m</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2.5</mn> <mo>&amp;le;</mo> <msub> <mi>a</mi> <mi>e</mi> </msub> <mo>&amp;le;</mo> <mn>25</mn> <mi>m</mi> <mi>m</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>&amp;GreaterEqual;</mo> <mn>0.99</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mn>2</mn> </msub> <mo>&amp;GreaterEqual;</mo> <mn>0.99</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>.</mo> </mrow>
  6. 6. according to the method for claim 1, it is characterised in that the step S2 includes：
    The minimal surface site error model established using approximate shceme Forecasting Methodology in the multi objective function optimization model.
  7. 7. according to the method for claim 6, it is characterised in that the multiple objective function is established using approximate shceme Forecasting Methodology Minimal surface site error model in Optimized model, including：
    Obtained using approximate shceme Forecasting Methodology and establish transfer matrix corresponding to the stability of milling parameter Stability Model；
    Judge the characteristic value of transfer matrix；
    If the characteristic value of transfer matrix is in Milling Process system stable region, when milling parameter Stability Model is established in acquisition Stable state coefficient；
    Minimal surface site error model is obtained according to the stable state coefficient.
  8. 8. according to the method for claim 7, it is characterised in that
    The minimal surface site error model is handled using Kriging model optimizations, obtains reliability, whether is judge reliability Meet Reliability Constraint condition, if satisfied, parameter corresponding to final result will be then tried to achieve, as the Milling Process technique after optimization Parameter.
  9. 9. according to the method for claim 8, it is characterised in that the minimal surface is handled using Kriging model optimizations Before the step of site error model, methods described also includes：
    Predetermined number sample point is obtained using mixed sampling method, the θ in initial Kriging models carried out using genetic algorithm Optimization, Kriging models are built using the θ after the predetermined number sample point and optimization.
  10. 10. according to the method for claim 9, it is characterised in that structure Kriging models, including：
    Judge whether the sampling dimension of minimal surface site error model is more than 1；
    If so, predetermined number sample point is then obtained using the Latin Hypercube Sampling method of amendment；
    Otherwise, predetermined number sample point is obtained using Han Mosili sequential samplings method；
    The maximum value position of the M-EI in minimal surface site error model is determined using improved global optimization method；
    Judge whether to meet stopping criterion, if so, then utilizing the θ structures Kriging after the predetermined number sample point and optimization Model；
    Otherwise, by it is determined that maximum value position at obtain sample point add sample set, rebuild Kriging models.
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CN111759488A (en) * 2020-07-09 2020-10-13 山东大学 Design method and system and preparation of variable cross-section nickel-titanium root canal file applied to root canal preparation
CN111759488B (en) * 2020-07-09 2021-08-24 山东大学 Design method and system and preparation of variable cross-section nickel-titanium root canal file applied to root canal preparation
CN114160847A (en) * 2020-09-10 2022-03-11 华中科技大学 Variable-rotation-speed processing method, system, equipment and medium
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CN112287484A (en) * 2020-10-29 2021-01-29 复旦大学 Complex engineering system reliability design method based on vector agent model
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CN113553727A (en) * 2021-08-12 2021-10-26 东北大学 Milling force coefficient identification method considering milling force amplitude and mean value simultaneously
CN113820999A (en) * 2021-09-26 2021-12-21 南昌航空大学 Stable milling process parameter optimization method based on neural network and genetic algorithm
CN113820999B (en) * 2021-09-26 2023-04-07 南昌航空大学 Stable milling process parameter optimization method based on neural network and genetic algorithm
CN114398732A (en) * 2022-01-11 2022-04-26 福州大学 CFRP milling process parameter optimization method and system
CN114548610A (en) * 2022-04-27 2022-05-27 季华实验室 Automatic arrangement method and device for engine cover outer plate stamping process
CN114548610B (en) * 2022-04-27 2022-07-08 季华实验室 Automatic arrangement method and device for engine cover outer plate stamping process

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